Internal generation of waves: Delta source function method and source term addition method |
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| Authors: | Gunwoo Kim Changhoon Lee Kyung-Duck Suh |
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| Institution: | aDepartment of Civil and Environmental Engineering, Seoul National University, San 56-1, Shinlim-dong, Gwanak-gu, Seoul 151-742, South Korea;bDepartment of Civil and Environmental Engineering, Sejong University, 98 Kunja-dong, Kwangjin-gu, Seoul 143-747, South Korea;cDepartment of Civil and Environmental Engineering & Engineering Research Institute, Seoul National University, San 56-1, Shinlim-dong, Gwanak-gu, Seoul 151-742, South Korea |
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| Abstract: | In this study, we investigate two internal wave generation methods in numerical modeling of time-dependent equations for water wave propagation, i.e., delta source function method and source term addition method, the latter of which has been called the line source method in literatures. We derive delta source functions for the Boussinesq-type equations and extended mild-slope equations. By applying the fractional step splitting method, we show that the delta source function method is equivalent to the source term addition method employing the energy velocity. This suggests that the energy velocity should be used rather than the phase velocity for the transport of incident wave energy in the source term addition method. Finally, the performance of the delta source function method is verified by accurately generating nonlinear cnoidal waves as well as linear waves for horizontally one-dimensional cases. |
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| Keywords: | Numerical generation of wave Internal generation of waves Source term addition Source function Energy velocity approach Boussinesq equations Extended mild-slope equations Numerical experiment |
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